Airfoil shape for a turbine bucket and turbine incorporating same

ABSTRACT

Third stage turbine buckets have airfoil profiles substantially in accordance with Cartesian coordinate values of X, Y and Z′ set forth Table I wherein X and Y values are in inches and the Z′ values are non-dimensional values from 0 to 1 convertible to Z distances in inches by multiplying the Z′ values by the height of the airfoil in inches and adding the radius of the airfoil base. The X and Y values are distances which, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z. The profile sections at each distance Z are joined smoothly to one another to form a complete airfoil shape. The X, Y and Z distances may be scalable as a function of the same constant or number to provide a scaled up or scaled down airfoil section for the bucket. The nominal airfoil given by the X, Y and Z distances lies within an envelope of +/−0.0.060 inches in directions normal to the surface of the airfoil.

BACKGROUND OF THE INVENTION

The present invention relates to an airfoil for a bucket of a stage of a gas turbine and particularly relates to a third stage turbine bucket airfoil profile.

Many system requirements must be met for each stage of the hot gas path section of a gas turbine in order to meet design goals including overall improved efficiency and airfoil loading. Particularly, the buckets of the third stage of the turbine section must meet the operating requirements for that particular stage and also be capable of efficient manufacture.

BRIEF DESCRIPTION OF THE INVENTION

The invention may be embodied in a turbine bucket including a bucket airfoil having an airfoil shape, said airfoil having a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z′ set forth in Table I wherein the Z′ values are non-dimensional values from 0 to 1 convertible to Z distances in inches by multiplying the Z′ values by airfoil height in inches and adding the radius of the airfoil base, and wherein X and Y are distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z, the profile sections at the Z distances being joined smoothly with one another to form a complete airfoil shape.

The invention may also be embodied in a turbine bucket including a bucket airfoil having an uncoated nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y and Z′ set forth in Table I wherein the Z′ values are non-dimensional values from 0 to 1 convertible to Z distances in inches by multiplying the Z′ values by the airfoil height in inches and adding the radius of the airfoil base, and wherein X and Y are distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each Z distance, the profile sections at the Z distances being joined smoothly with one another to form a complete airfoil shape, the X, Y and Z distances being scalable as a function of the same constant or number to provide a scaled-up or scaled-down airfoil.

The invention may further be embodied in a turbine comprising a turbine wheel having a plurality of buckets, each of said buckets including an airfoil having an airfoil shape, said airfoil having a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z′ set forth in Table I wherein the Z′ values are non-dimensional values from 0 to 1 convertible to Z distances in inches by multiplying the Z′ values by the airfoil height in inches and adding the radius of the airfoil base, and wherein X and Y are distances in inches which, when connected by smooth continuing arcs, define the airfoil profile sections at each distance Z, the profile sections at the Z distances being joined smoothly with one another to form a complete airfoil shape.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other objects and advantages of this invention, will be more completely understood and appreciated by careful study of the following more detailed description of the presently preferred example embodiments of the invention taken in conjunction with the accompanying drawings, in which:

FIG. 1 is a schematic representation of a hot gas path through multiple stages of a gas turbine and illustrates a third stage bucket airfoil according to an example embodiment of the present invention; and

FIG. 2 is a perspective view of a bucket according to an example embodiment of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

Referring now to the drawings, particularly to FIG. 1, there is illustrated a hot gas path, generally designated 10, of a gas turbine 12 including a plurality of turbine stages. Three stages are illustrated. For example, the first stage comprises a plurality of circumferentially spaced nozzles 14 and buckets 16. The nozzles are circumferentially spaced one from the other and fixed about the axis of the rotor. The first stage buckets 16, of course, are mounted on the turbine rotor 17. A second stage of the turbine 12 is also illustrated, including a plurality of circumferentially spaced nozzles 18 and a plurality of circumferentially spaced buckets 20 mounted on the rotor. The third stage is also illustrated including a plurality of circumferentially spaced nozzles 22 and buckets 24 mounted on rotor 17. It will be appreciated that the nozzles and buckets lie in the hot gas path 10 of the turbine, the direction of flow of the hot gas through the hot gas path 10 being indicated by the arrow 26.

Referring to FIG. 2, it will be appreciated that the buckets, for example, the buckets 24 of the third stage have a bucket root 32 mounted on a rotor wheel, not shown in detail, forming part of rotor 17 and include platforms 30. It will also be appreciated that each bucket 24 has a bucket airfoil 34 as illustrated in FIG. 2. Thus, each of the buckets 24 has a bucket airfoil profile at any cross-section from the bucket platform to the bucket tip 36 in the shape of an airfoil 34. The base 38 of the bucket airfoil, for purposes of defining the coordinate system in an example embodiment of the turbine, lies at 37.3182 inches along a radius from the turbine centerline. This corresponds to the non-dimensional Z′ value of Table I at Z′ equals 0.000. The tip 36 of the bucket airfoil, for purposes of defining the airfoil shape in an example embodiment of the turbine, lies at 54.9318 inches along a radius from the turbine centerline. Thus, the Z length of the bucket 24 is 17.6136 inches from root to tip.

The 7FB Integrated Gasification Combined Cycle (IGCC) gas turbine hot gas path requires a third stage airfoil that meets system requirements of aerodynamic and mechanical blade loading and efficiency. To define the airfoil shape of each third stage bucket airfoil, there is a unique set or loci of points in space that meet the stage requirements and can be manufactured. This unique loci of points meets the requirements for stage efficiency and are arrived at by iteration between aerodynamic and mechanical loadings enabling the turbine to run in an efficient, safe and smooth manner. These points are unique and specific to the system and are not obvious to those skilled in the art. The loci which defines the bucket airfoil profile of the invention comprises a set of 3,200 points with X, Y and Z′ dimensions relative to the reference origin coordinate system established as shown in FIG. 2. More specifically, the coordinate system is set relative to the airfoil and is fully defined by points A, B and C. Points A and B are both located 37.3182 inches above the cold rotor centerline. Point A lies on the leading-edge airfoil surface and Point B lies on the trailing-edge airfoil surface. Point C is located 54.9318 inches above the cold rotor centerline on the airfoil trailing-edge surface. Points A and B define the X—axis. Points A, B and C define the X-Z plane. The coordinate system origin is located between Points A and B as schematically shown in FIG. 2. As mentioned above, the Cartesian coordinate system of X, Y and Z′ values given in Table I below defines the profile of the bucket airfoil at various locations along its length. The coordinate values for the X and Y coordinates are set forth in inches in Table I although other units of dimensions may be used when the values are appropriately converted. The Z values are set forth in Table I in non-dimensional form (Z′) from 0 to 1. To convert the Z′ value to a Z coordinate value, e.g., in inches, the non-dimensional Z′ value given in Table I is multiplied by the Z length of the airfoil in inches (17.6136 in this example embodiment) and adding the radius of the airfoil base (37.3182 in this example embodiment). As described above, the Cartesian coordinate system has orthogonally-related X, Y and Z axes and the X axis lies parallel to the turbine rotor centerline, i.e., the rotary axis and a positive X coordinate value is axial toward the aft, i.e., exhaust end of the turbine. The positive Y coordinate value extends tangentially in the direction of rotation of the rotor and the positive Z′ coordinate value is radially outwardly toward the bucket tip.

By defining X and Y coordinate values at selected locations in a Z direction normal to the X, Y plane, the profile section of the bucket airfoil, at each Z distance along the length of the airfoil can be ascertained. By connecting the X and Y values with smooth continuing arcs, each profile section at each distance Z is fixed. The airfoil profiles of the various surface locations between the distances Z are determined by smoothly connecting the adjacent profile sections to one another to form the airfoil profile.

The Table I values are generated and shown to four decimal places for determining the profile of the airfoil. As the blade heats up in surface, stress and temperature will cause a change in the X, Y and Z's. Accordingly, the values for the profile given in Table I represent ambient, non-operating or non-hot conditions and are for an uncoated airfoil.

There are typical manufacturing tolerances as well as coatings which must be accounted for in the actual profile of the airfoil. Each section is joined smoothly with the other sections to form the complete airfoil shape. It will therefore be appreciated that +/− typical manufacturing tolerances, i.e., +/− values, including any coating thicknesses, are additive to the X and Y values given in Table I below. Accordingly, a distance of +/−0.060 inches in a direction normal to any surface location along the airfoil profile defines an airfoil profile envelope for this particular bucket airfoil design and turbine, i.e., a range of variation between measured points on the actual airfoil surface at nominal cold or room temperature and the ideal position of those points as given in the Table below at the same temperature. The bucket airfoil design is robust to this range of variation without impairment of mechanical and aerodynamic functions.

TABLE I # X Y Z′ 1 −2.5601 −0.3071 0.0000 2 −2.7836 −0.0184 0.0000 3 −2.2685 0.3689 0.0000 4 −2.4327 −0.2845 0.0000 5 −2.8627 −0.1207 0.0000 6 −2.3803 0.3036 0.0000 7 −2.3057 −0.2592 0.0000 8 −2.9068 −0.2406 0.0000 9 −2.4887 0.2329 0.0000 10 −2.8176 −0.3190 0.0000 11 −2.5930 0.1562 0.0000 12 −2.6886 −0.3228 0.0000 13 −2.6920 0.0729 0.0000 14 −1.2858 −0.0828 0.0000 15 −1.9251 −0.1823 0.0000 16 −1.6744 0.6228 0.0000 17 −1.5503 0.6599 0.0000 18 −1.7978 −0.1587 0.0000 19 −1.7969 0.5812 0.0000 20 −1.6703 −0.1368 0.0000 21 −1.9179 0.5352 0.0000 22 −1.5424 −0.1167 0.0000 23 −2.1790 −0.2331 0.0000 24 −2.0370 0.4845 0.0000 25 −1.4251 0.6925 0.0000 26 −1.4142 −0.0987 0.0000 27 −2.0521 −0.2072 0.0000 28 −2.1540 0.4291 0.0000 29 −0.6401 −0.0426 0.0000 30 −1.0434 0.7631 0.0000 31 −0.3976 0.7861 0.0000 32 −0.5107 −0.0435 0.0000 33 −1.1570 −0.0693 0.0000 34 −1.1715 0.7442 0.0000 35 −0.5269 0.7915 0.0000 36 −0.3813 −0.0478 0.0000 37 −1.0280 −0.0583 0.0000 38 −1.2987 0.7206 0.0000 39 −0.6564 0.7917 0.0000 40 −0.8989 −0.0501 0.0000 41 −0.7857 0.7870 0.0000 42 −0.7695 −0.0448 0.0000 43 −0.9148 0.7775 0.0000 44 0.2392 0.6779 0.0000 45 0.1337 −0.0987 0.0000 46 0.1140 0.7107 0.0000 47 −0.0126 0.7378 0.0000 48 0.2613 −0.1201 0.0000 49 0.6402 −0.2050 0.0000 50 0.3884 −0.1449 0.0000 51 0.6046 0.5472 0.0000 52 −0.2521 −0.0554 0.0000 53 −0.2686 0.7754 0.0000 54 −0.1402 0.7594 0.0000 55 0.5147 −0.1732 0.0000 56 0.4847 0.5960 0.0000 57 −0.1231 −0.0664 0.0000 58 0.3629 0.6397 0.0000 59 0.0055 −0.0808 0.0000 60 1.4833 0.0051 0.0000 61 1.3688 −0.4708 0.0000 62 0.7647 −0.2403 0.0000 63 0.8378 0.4350 0.0000 64 1.3810 0.0844 0.0000 65 0.9510 0.3722 0.0000 66 1.4849 −0.5279 0.0000 67 0.8882 −0.2791 0.0000 68 0.7223 0.4934 0.0000 69 1.2768 0.1612 0.0000 70 1.7797 −0.2456 0.0000 71 1.5993 −0.5885 0.0000 72 1.0104 −0.3216 0.0000 73 1.1704 0.2349 0.0000 74 1.6825 −0.1602 0.0000 75 1.7118 −0.6526 0.0000 76 1.1314 −0.3676 0.0000 77 1.0618 0.3054 0.0000 78 1.5837 −0.0765 0.0000 79 1.8222 −0.7200 0.0000 80 1.2509 −0.4174 0.0000 81 1.9702 −0.4210 0.0000 82 2.4302 −0.8761 0.0000 83 2.7492 −1.3739 0.0000 84 2.0371 −0.8644 0.0000 85 2.4431 −1.1854 0.0000 86 1.9307 −0.7907 0.0000 87 1.8756 −0.3326 0.0000 88 2.3391 −0.7842 0.0000 89 2.7790 −1.2583 0.0000 90 2.5386 −1.2728 0.0000 91 2.2478 −0.6925 0.0000 92 2.6310 −1.3634 0.0000 93 2.1414 −0.9411 0.0000 94 2.1561 −0.6011 0.0000 95 2.6097 −1.0627 0.0000 96 2.6967 −1.1585 0.0000 97 2.2440 −1.0200 0.0000 98 2.0637 −0.5105 0.0000 99 2.5207 −0.9687 0.0000 100 2.3447 −1.1013 0.0000 101 −2.5943 −0.2386 0.0323 102 −2.5933 0.1518 0.0323 103 −2.4700 −0.2241 0.0323 104 −2.6816 0.0631 0.0323 105 −2.3464 −0.2041 0.0323 106 −2.2898 0.3719 0.0323 107 −2.2231 −0.1824 0.0323 108 −2.7986 −0.1534 0.0323 109 −2.3956 0.3051 0.0323 110 −2.7191 −0.2345 0.0323 111 −2.4972 0.2320 0.0323 112 −2.7566 −0.0369 0.0323 113 −1.9763 −0.1408 0.0323 114 −2.0686 0.4889 0.0323 115 −1.4785 0.6945 0.0323 116 −1.8525 −0.1221 0.0323 117 −2.1806 0.4331 0.0323 118 −1.5996 0.6628 0.0323 119 −1.7284 −0.1054 0.0323 120 −1.7193 0.6264 0.0323 121 −1.6041 −0.0907 0.0323 122 −1.8376 0.5854 0.0323 123 −1.4796 −0.0781 0.0323 124 −2.0998 −0.1610 0.0323 125 −1.9541 0.5396 0.0323 126 −1.3563 0.7216 0.0323 127 −1.3548 −0.0676 0.0323 128 −0.8600 0.7845 0.0323 129 −0.6043 −0.0525 0.0323 130 −1.2299 −0.0593 0.0323 131 −0.9848 0.7756 0.0323 132 −0.3599 0.7726 0.0323 133 −0.4792 −0.0585 0.0323 134 −1.1049 −0.0533 0.0323 135 −1.1093 0.7622 0.0323 136 −0.4846 0.7828 0.0323 137 −0.3543 −0.0672 0.0323 138 −0.9797 −0.0495 0.0323 139 −1.2331 0.7442 0.0323 140 −0.6097 0.7881 0.0323 141 −0.8546 −0.0480 0.0323 142 −0.7348 0.7887 0.0323 143 −0.7294 −0.0490 0.0323 144 −0.2356 0.7573 0.0323 145 0.6307 −0.2388 0.0323 146 0.3695 0.6022 0.0323 147 0.0187 −0.1095 0.0323 148 0.2514 0.6437 0.0323 149 0.1424 −0.1293 0.0323 150 0.1316 0.6801 0.0323 151 0.2655 −0.1520 0.0323 152 −0.1053 −0.0926 0.0323 153 0.0104 0.7111 0.0323 154 0.3880 −0.1777 0.0323 155 0.5999 0.5044 0.0323 156 −0.2297 −0.0785 0.0323 157 −0.1121 0.7368 0.0323 158 0.5098 −0.2066 0.0323 159 0.4857 0.5557 0.0323 160 1.7645 −0.7569 0.0323 161 1.1037 −0.4023 0.0323 162 1.2184 −0.4524 0.0323 163 0.9294 0.3245 0.0323 164 1.4356 −0.0427 0.0323 165 1.3314 −0.5063 0.0323 166 0.7508 −0.2744 0.0323 167 0.8218 0.3885 0.0323 168 1.3383 0.0360 0.0323 169 1.8091 −0.3761 0.0323 170 1.4426 −0.5638 0.0323 171 0.8697 −0.3134 0.0323 172 0.7119 0.4485 0.0323 173 1.2391 0.1124 0.0323 174 1.7178 −0.2904 0.0323 175 1.5519 −0.6248 0.0323 176 0.9874 −0.3560 0.0323 177 1.1380 0.1862 0.0323 178 1.6252 −0.2062 0.0323 179 1.6592 −0.6893 0.0323 180 1.0347 0.2570 0.0323 181 1.5312 −0.1235 0.0323 182 2.4222 −1.0020 0.0323 183 2.5384 −1.3900 0.0323 184 2.2630 −1.1348 0.0323 185 1.8991 −0.4631 0.0323 186 2.3363 −0.9110 0.0323 187 2.6519 −1.3970 0.0323 188 2.3574 −1.2170 0.0323 189 1.8678 −0.8276 0.0323 190 2.2498 −0.8205 0.0323 191 2.6703 −1.2838 0.0323 192 2.4493 −1.3020 0.0323 193 1.9692 −0.9011 0.0323 194 2.1631 −0.7302 0.0323 195 2.5899 −1.1879 0.0323 196 2.0686 −0.9771 0.0323 197 2.0759 −0.6403 0.0323 198 2.5069 −1.0942 0.0323 199 2.1666 −1.0550 0.0323 200 1.9880 −0.5512 0.0323 201 −2.4067 0.3012 0.0645 202 −2.5038 −0.1601 0.0645 203 −2.5002 0.2240 0.0645 204 −2.3834 −0.1468 0.0645 205 −2.5855 0.1380 0.0645 206 −2.3076 0.3709 0.0645 207 −2.2634 −0.1292 0.0645 208 −2.6572 0.0404 0.0645 209 −2.6966 −0.0730 0.0645 210 −2.6246 −0.1559 0.0645 211 −1.8756 0.5895 0.0645 212 −1.9031 −0.0793 0.0645 213 −1.9876 0.5431 0.0645 214 −1.4106 0.7254 0.0645 215 −1.7825 −0.0666 0.0645 216 −2.0972 0.4914 0.0645 217 −1.5288 0.6986 0.0645 218 −1.6617 −0.0563 0.0645 219 −2.2041 0.4341 0.0645 220 −1.6459 0.6671 0.0645 221 −1.5407 −0.0483 0.0645 222 −2.1435 −0.1111 0.0645 223 −1.7616 0.6307 0.0645 224 −1.4196 −0.0427 0.0645 225 −2.0234 −0.0942 0.0645 226 −1.1772 −0.0378 0.0645 227 −1.2914 0.7475 0.0645 228 −0.6875 0.7892 0.0645 229 −0.6925 −0.0522 0.0645 230 −1.2984 −0.0392 0.0645 231 −0.8087 0.7900 0.0645 232 −0.5715 −0.0607 0.0645 233 −0.9299 0.7862 0.0645 234 −0.4507 −0.0712 0.0645 235 −1.0559 −0.0384 0.0645 236 −1.0508 0.7778 0.0645 237 −0.4455 0.7740 0.0645 238 −0.3301 −0.0837 0.0645 239 −0.9347 −0.0410 0.0645 240 −1.1714 0.7650 0.0645 241 −0.5663 0.7839 0.0645 242 −0.8136 −0.0456 0.0645 243 −0.0868 0.7152 0.0645 244 0.5041 −0.2356 0.0645 245 0.4853 0.5181 0.0645 246 −0.0897 −0.1151 0.0645 247 −0.2055 0.7397 0.0645 248 0.6209 −0.2682 0.0645 249 0.3745 0.5671 0.0645 250 0.0300 −0.1341 0.0645 251 0.5941 0.4646 0.0645 252 −0.3252 0.7593 0.0645 253 0.2616 0.6116 0.0645 254 0.1494 −0.1555 0.0645 255 0.1470 0.6511 0.0645 256 0.2683 −0.1795 0.0645 257 0.0308 0.6857 0.0645 258 0.3865 −0.2061 0.0645 259 −0.2098 −0.0983 0.0645 260 1.6090 −0.7217 0.0645 261 1.0768 −0.4329 0.0645 262 1.0080 0.2124 0.0645 263 1.4807 −0.1666 0.0645 264 1.7095 −0.7895 0.0645 265 0.9077 0.2805 0.0645 266 0.7367 −0.3041 0.0645 267 1.3896 −0.0866 0.0645 268 1.8080 −0.8601 0.0645 269 1.2955 −0.5376 0.0645 270 0.8053 0.3455 0.0645 271 1.2969 −0.0084 0.0645 272 1.7457 −0.4157 0.0645 273 1.4020 −0.5955 0.0645 274 0.8514 −0.3434 0.0645 275 0.7008 0.4069 0.0645 276 1.2025 0.0676 0.0645 277 1.6587 −0.3313 0.0645 278 1.5065 −0.6569 0.0645 279 1.1870 −0.4833 0.0645 280 0.9648 −0.3863 0.0645 281 1.1062 0.1413 0.0645 282 1.5704 −0.2482 0.0645 283 2.0933 −1.0858 0.0645 284 1.9162 −0.5881 0.0645 285 2.3296 −1.0315 0.0645 286 2.4508 −1.4132 0.0645 287 2.1857 −1.1643 0.0645 288 1.8315 −0.5014 0.0645 289 2.2479 −0.9420 0.0645 290 2.5599 −1.4167 0.0645 291 2.2764 −1.2447 0.0645 292 2.1656 −0.8530 0.0645 293 2.5676 −1.3066 0.0645 294 2.3649 −1.3276 0.0645 295 1.9047 −0.9333 0.0645 296 2.0830 −0.7641 0.0645 297 2.4898 −1.2136 0.0645 298 1.9996 −1.0087 0.0645 299 2.0000 −0.6758 0.0645 300 2.4104 −1.1220 0.0645 301 −2.5343 −0.0847 0.0968 302 −2.3208 0.3622 0.0968 303 −2.4172 −0.0892 0.0968 304 −2.4120 0.2879 0.0968 305 −2.3002 −0.0770 0.0968 306 −2.4948 0.2045 0.0968 307 −2.5637 0.1094 0.0968 308 −2.6006 −0.0012 0.0968 309 −1.3624 −0.0122 0.0968 310 −1.9498 −0.0349 0.0968 311 −1.8009 0.6328 0.0968 312 −1.8326 −0.0250 0.0968 313 −1.9105 0.5903 0.0968 314 −1.7152 −0.0179 0.0968 315 −2.0179 0.5423 0.0968 316 −1.4617 0.7294 0.0968 317 −1.5976 −0.0135 0.0968 318 −2.1835 −0.0619 0.0968 319 −2.1226 0.4886 0.0968 320 −1.5761 0.7022 0.0968 321 −1.4800 −0.0117 0.0968 322 −2.0668 −0.0474 0.0968 323 −2.2238 0.4288 0.0968 324 −1.6893 0.6700 0.0968 325 −1.1130 0.7823 0.0968 326 −0.5257 0.7788 0.0968 327 −0.7752 −0.0437 0.0968 328 −1.2299 0.7694 0.0968 329 −0.6429 0.7884 0.0968 330 −0.6581 −0.0549 0.0968 331 −1.2448 −0.0148 0.0968 332 −0.5411 −0.0677 0.0968 333 −0.7605 0.7936 0.0968 334 −1.3462 0.7518 0.0968 335 −1.1272 −0.0194 0.0968 336 −0.8781 0.7943 0.0968 337 −0.4243 −0.0819 0.0968 338 −1.0097 −0.0259 0.0968 339 −0.9957 0.7906 0.0968 340 −0.4089 0.7646 0.0968 341 −0.8924 −0.0340 0.0968 342 0.0496 0.6614 0.0968 343 0.3852 −0.2300 0.0968 344 −0.1914 −0.1150 0.0968 345 0.1610 0.6237 0.0968 346 −0.0633 0.6943 0.0968 347 0.4989 −0.2601 0.0968 348 0.4844 0.4829 0.0968 349 −0.0753 −0.1340 0.0968 350 −0.1775 0.7225 0.0968 351 0.6118 −0.2932 0.0968 352 0.3786 0.5342 0.0968 353 0.0405 −0.1548 0.0968 354 0.5882 0.4275 0.0968 355 −0.2928 0.7459 0.0968 356 0.2707 0.5812 0.0968 357 0.1559 −0.1776 0.0968 358 0.2708 −0.2026 0.0968 359 −0.3078 −0.0976 0.0968 360 1.4642 −0.6848 0.0968 361 0.9439 −0.4123 0.0968 362 1.0761 0.1001 0.0968 363 1.5190 −0.2866 0.0968 364 1.5622 −0.7499 0.0968 365 1.0517 −0.4593 0.0968 366 0.9825 0.1714 0.0968 367 1.4334 −0.2059 0.0968 368 1.3464 −0.1267 0.0968 369 1.6583 −0.8178 0.0968 370 1.1578 −0.5101 0.0968 371 1.7684 −0.5362 0.0968 372 1.7524 −0.8884 0.0968 373 0.8870 0.2400 0.0968 374 1.2620 −0.5647 0.0968 375 0.7237 −0.3294 0.0968 376 0.7894 0.3058 0.0968 377 1.2579 −0.0491 0.0968 378 1.6864 −0.4519 0.0968 379 1.3641 −0.6230 0.0968 380 0.8345 −0.3690 0.0968 381 0.6899 0.3684 0.0968 382 1.1679 0.0266 0.0968 383 1.6033 −0.3686 0.0968 384 1.9354 −1.0362 0.0968 385 1.9293 −0.7078 0.0968 386 2.3212 −1.1464 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0.1613 579 0.8522 0.1686 0.1613 580 1.2719 −0.1967 0.1613 581 1.6589 −0.5968 0.1613 582 1.1104 −0.5513 0.1613 583 1.2069 −0.6068 0.1613 584 0.7632 0.2356 0.1613 585 0.9113 −0.4516 0.1613 586 1.9525 −0.9316 0.1613 587 2.3082 −1.3598 0.1613 588 2.1491 −1.3849 0.1613 589 2.0696 −1.3069 0.1613 590 1.8800 −0.8471 0.1613 591 2.2386 −1.2729 0.1613 592 1.8250 −1.0795 0.1613 593 1.8069 −0.7631 0.1613 594 1.9073 −1.1545 0.1613 595 2.2270 −1.4644 0.1613 596 2.0967 −1.1013 0.1613 597 1.9889 −1.2302 0.1613 598 2.0248 −1.0163 0.1613 599 2.3244 −1.4596 0.1613 600 2.1681 −1.1867 0.1613 601 −2.3469 0.1519 0.1935 602 −1.5293 0.0711 0.1935 603 −2.0717 0.0726 0.1935 604 −2.2493 0.3412 0.1935 605 −1.8003 0.6396 0.1935 606 −1.4211 0.0617 0.1935 607 −1.9633 0.0790 0.1935 608 −2.3141 0.2542 0.1935 609 −1.8987 0.5937 0.1935 610 −1.8548 0.0822 0.1935 611 −1.9940 0.5417 0.1935 612 −1.4916 0.7426 0.1935 613 −1.7462 0.0818 0.1935 614 −2.2881 0.0716 0.1935 615 −2.0853 0.4829 0.1935 616 −1.5963 0.7138 0.1935 617 −1.6376 0.0779 0.1935 618 −2.1801 0.0656 0.1935 619 −2.1713 0.4166 0.1935 620 −1.6993 0.6795 0.1935 621 −0.7369 0.8014 0.1935 622 −1.0625 0.8058 0.1935 623 −1.3856 0.7661 0.1935 624 −0.8453 0.8076 0.1935 625 −0.9539 0.8091 0.1935 626 −0.5213 0.7756 0.1935 627 −1.1708 0.7976 0.1935 628 −0.6288 0.7907 0.1935 629 −1.2785 0.7844 0.1935 630 −0.8830 −0.0106 0.1935 631 −0.7758 −0.0283 0.1935 632 −1.3131 0.0502 0.1935 633 −0.6688 −0.0466 0.1935 634 −1.2053 0.0369 0.1935 635 −0.5618 −0.0656 0.1935 636 −1.0977 0.0222 0.1935 637 −0.4550 −0.0851 0.1935 638 −0.9902 0.0063 0.1935 639 −0.2037 0.7039 0.1935 640 0.2985 0.4998 0.1935 641 0.1825 −0.2196 0.1935 642 −0.3483 −0.1053 0.1935 643 0.2015 0.5488 0.1935 644 0.2877 −0.2467 0.1935 645 −0.2417 −0.1261 0.1935 646 −0.4145 0.7560 0.1935 647 0.1027 0.5938 0.1935 648 0.3922 −0.2760 0.1935 649 0.5774 0.3317 0.1935 650 −0.1353 −0.1478 0.1935 651 0.4864 0.3910 0.1935 652 0.0021 0.6347 0.1935 653 0.4961 −0.3077 0.1935 654 −0.0291 −0.1704 0.1935 655 −0.1001 0.6714 0.1935 656 0.5991 −0.3422 0.1935 657 0.3935 0.4472 0.1935 658 0.0769 −0.1942 0.1935 659 −0.3086 0.7321 0.1935 660 0.7534 0.2045 0.1935 661 0.6664 0.2694 0.1935 662 0.9222 0.0678 0.1935 663 0.8387 0.1372 0.1935 664 1.1857 −0.6227 0.1935 665 1.6184 −0.9498 0.1935 666 0.7009 −0.3799 0.1935 667 1.5401 −0.5421 0.1935 668 1.6994 −1.0222 0.1935 669 1.2765 −0.6822 0.1935 670 0.8014 −0.4210 0.1935 671 1.0844 −0.0767 0.1935 672 1.4668 −0.4619 0.1935 673 1.1633 −0.1513 0.1935 674 1.3651 −0.7451 0.1935 675 0.9004 −0.4658 0.1935 676 1.3926 −0.3827 0.1935 677 1.4514 −0.8109 0.1935 678 0.9975 −0.5143 0.1935 679 1.0040 −0.0036 0.1935 680 1.3173 −0.3044 0.1935 681 1.6842 −0.7046 0.1935 682 1.5358 −0.8793 0.1935 683 1.0927 −0.5666 0.1935 684 1.2409 −0.2273 0.1935 685 1.6126 −0.6230 0.1935 686 1.9653 −1.0358 0.1935 687 2.2605 −1.4696 0.1935 688 2.0141 −1.3216 0.1935 689 1.8956 −0.9525 0.1935 690 2.2395 −1.3727 0.1935 691 2.0908 −1.3984 0.1935 692 1.7552 −0.7868 0.1935 693 1.8256 −0.8695 0.1935 694 2.1721 −1.2876 0.1935 695 2.1664 −1.4764 0.1935 696 1.7790 −1.0960 0.1935 697 2.1037 −1.2032 0.1935 698 1.8580 −1.1706 0.1935 699 2.0348 −1.1193 0.1935 700 1.9363 −1.2458 0.1935 701 −2.0989 0.4428 0.2258 702 −1.6356 0.6955 0.2258 703 −1.4734 0.0861 0.2258 704 −2.0029 0.1062 0.2258 705 −2.1760 0.3701 0.2258 706 −1.7346 0.6574 0.2258 707 −1.8969 0.1095 0.2258 708 −1.8311 0.6134 0.2258 709 −1.7908 0.1089 0.2258 710 −2.2731 0.1864 0.2258 711 −1.9246 0.5634 0.2258 712 −2.1089 0.1015 0.2258 713 −2.2404 0.2860 0.2258 714 −1.6848 0.1045 0.2258 715 −2.2144 0.1085 0.2258 716 −2.0143 0.5068 0.2258 717 −1.5346 0.7280 0.2258 718 −1.5790 0.0967 0.2258 719 −1.1179 0.8043 0.2258 720 −0.5889 0.7863 0.2258 721 −0.9489 0.0080 0.2258 722 −1.2234 0.7930 0.2258 723 −0.6942 0.7993 0.2258 724 −0.8444 −0.0105 0.2258 725 −1.0120 0.8104 0.2258 726 −1.3681 0.0733 0.2258 727 −1.3282 0.7767 0.2258 728 −0.7999 0.8078 0.2258 729 −0.7401 −0.0295 0.2258 730 −1.2630 0.0588 0.2258 731 −0.5316 −0.0689 0.2258 732 −1.4320 0.7550 0.2258 733 −0.4275 −0.0893 0.2258 734 −0.9060 0.8115 0.2258 735 −0.6358 −0.0490 0.2258 736 −1.1582 0.0429 0.2258 737 −0.4843 0.7686 0.2258 738 −1.0535 0.0259 0.2258 739 0.3080 0.4755 0.2258 740 −0.0761 0.6548 0.2258 741 0.0910 −0.2013 0.2258 742 −0.1763 0.6896 0.2258 743 0.1938 −0.2271 0.2258 744 −0.3235 −0.1101 0.2258 745 0.3993 0.4215 0.2258 746 −0.2778 0.7203 0.2258 747 0.2148 0.5260 0.2258 748 −0.3806 0.7466 0.2258 749 −0.2196 −0.1316 0.2258 750 0.1196 0.5729 0.2258 751 0.0226 0.6158 0.2258 752 0.4886 0.3642 0.2258 753 −0.0123 −0.1769 0.2258 754 −0.1158 −0.1538 0.2258 755 0.5992 −0.3521 0.2258 756 0.2963 −0.2548 0.2258 757 0.4991 −0.3169 0.2258 758 0.3981 −0.2846 0.2258 759 1.0774 −0.5796 0.2258 760 0.8267 0.1082 0.2258 761 0.8915 −0.4776 0.2258 762 1.1672 −0.6361 0.2258 763 0.6981 −0.3904 0.2258 764 0.7449 0.1757 0.2258 765 1.1383 −0.1798 0.2258 766 1.0625 −0.1055 0.2258 767 0.5760 0.3040 0.2258 768 0.7956 −0.4322 0.2258 769 0.6614 0.2411 0.2258 770 0.9854 −0.0326 0.2258 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0.5027 0.5806 1817 −1.5658 0.8436 0.5806 1818 −1.1424 0.9596 0.5806 1819 −0.7050 0.9174 0.5806 1820 −0.8020 0.2885 0.5806 1821 −1.2006 0.4773 0.5806 1822 −1.6362 0.5313 0.5806 1823 −1.6430 0.8008 0.5806 1824 −1.2301 0.9491 0.5806 1825 −0.7909 0.9379 0.5806 1826 −0.7250 0.2453 0.5806 1827 −1.1180 0.4461 0.5806 1828 −1.4020 0.9091 0.5806 1829 −1.5478 0.5313 0.5806 1830 −0.4573 0.8244 0.5806 1831 −0.2673 −0.0218 0.5806 1832 −0.5380 0.8602 0.5806 1833 −0.1548 0.6427 0.5806 1834 −0.1914 −0.0670 0.5806 1835 −0.5719 0.1572 0.5806 1836 −0.6206 0.8913 0.5806 1837 −0.2273 0.6931 0.5806 1838 −0.1156 −0.1125 0.5806 1839 −0.4956 0.1127 0.5806 1840 −0.3019 0.7404 0.5806 1841 −0.4194 0.0680 0.5806 1842 −0.3786 0.7843 0.5806 1843 −0.3433 0.0232 0.5806 1844 −0.0843 0.5895 0.5806 1845 0.1100 −0.2515 0.5806 1846 0.3318 −0.3963 0.5806 1847 0.1791 0.3544 0.5806 1848 0.1844 −0.2989 0.5806 1849 0.2584 −0.3472 0.5806 1850 0.2408 0.2912 0.5806 1851 0.0509 0.4759 0.5806 1852 −0.0401 −0.1583 0.5806 1853 0.1158 0.4160 0.5806 1854 −0.0158 0.5338 0.5806 1855 0.3012 0.2267 0.5806 1856 0.0351 −0.2046 0.5806 1857 0.8213 −0.7734 0.5806 1858 0.4764 −0.4978 0.5806 1859 0.5312 −0.0414 0.5806 1860 0.8036 −0.3890 0.5806 1861 0.8870 −0.8324 0.5806 1862 0.5474 −0.5504 0.5806 1863 0.4751 0.0268 0.5806 1864 0.7499 −0.3189 0.5806 1865 0.9516 −0.8926 0.5806 1866 0.6175 −0.6041 0.5806 1867 0.4182 0.0943 0.5806 1868 0.6959 −0.2490 0.5806 1869 0.9640 −0.6000 0.5806 1870 1.0152 −0.9539 0.5806 1871 0.6865 −0.6592 0.5806 1872 0.3602 0.1610 0.5806 1873 0.6415 −0.1794 0.5806 1874 0.9106 −0.5296 0.5806 1875 0.7545 −0.7156 0.5806 1876 0.4045 −0.4465 0.5806 1877 0.5866 −0.1102 0.5806 1878 0.8571 −0.4593 0.5806 1879 1.4448 −1.3986 0.5806 1880 1.1399 −1.0791 0.5806 1881 1.0708 −0.7406 0.5806 1882 1.3396 −1.0910 0.5806 1883 1.6101 −1.4402 0.5806 1884 1.5048 −1.4634 0.5806 1885 1.2013 −1.1425 0.5806 1886 1.0174 −0.6703 0.5806 1887 1.2856 −1.0212 0.5806 1888 1.5566 −1.3699 0.5806 1889 1.5647 −1.5283 0.5806 1890 1.2625 −1.2062 0.5806 1891 1.3843 −1.3342 0.5806 1892 1.2317 −0.9512 0.5806 1893 1.5024 −1.3001 0.5806 1894 1.3235 −1.2701 0.5806 1895 1.1780 −0.8811 0.5806 1896 1.4480 −1.2305 0.5806 1897 1.0779 −1.0162 0.5806 1898 1.1244 −0.8109 0.5806 1899 1.3938 −1.1608 0.5806 1900 1.6385 −1.5181 0.5806 1901 −1.6923 0.7915 0.6129 1902 −1.7523 0.7286 0.6129 1903 −1.7553 0.6458 0.6129 1904 −1.6898 0.5928 0.6129 1905 −0.7111 0.2814 0.6129 1906 −1.0930 0.4916 0.6129 1907 −1.2967 0.9665 0.6129 1908 −0.8630 0.9737 0.6129 1909 −0.6371 0.2350 0.6129 1910 −1.0140 0.4545 0.6129 1911 −1.4289 0.5799 0.6129 1912 −1.3814 0.9454 0.6129 1913 −0.9495 0.9853 0.6129 1914 −0.9367 0.4141 0.6129 1915 −1.4641 0.9177 0.6129 1916 −1.0366 0.9904 0.6129 1917 −0.8606 0.3713 0.6129 1918 −1.2571 0.5507 0.6129 1919 −1.5443 0.8833 0.6129 1920 −1.1238 0.9890 0.6129 1921 −0.6936 0.9323 0.6129 1922 −1.3422 0.5696 0.6129 1923 −1.2107 0.9811 0.6129 1924 −1.5161 0.5827 0.6129 1925 −0.7855 0.3269 0.6129 1926 −1.1739 0.5242 0.6129 1927 −1.6033 0.5828 0.6129 1928 −1.6210 0.8418 0.6129 1929 −0.7776 0.9559 0.6129 1930 −0.3767 0.7878 0.6129 1931 −0.3439 0.0457 0.6129 1932 −0.4528 0.8305 0.6129 1933 −0.2709 −0.0022 0.6129 1934 −0.1981 −0.0503 0.6129 1935 −0.5635 0.1881 0.6129 1936 −0.6114 0.9032 0.6129 1937 −0.2310 0.6918 0.6129 1938 −0.1255 −0.0987 0.6129 1939 −0.4901 0.1409 0.6129 1940 −0.3028 0.7414 0.6129 1941 −0.4169 0.0934 0.6129 1942 −0.5310 0.8691 0.6129 1943 0.1627 −0.2957 0.6129 1944 −0.0275 0.5273 0.6129 1945 0.2781 0.2161 0.6129 1946 0.0192 −0.1964 0.6129 1947 −0.0934 0.5845 0.6129 1948 0.2197 0.2811 0.6129 1949 0.0911 −0.2458 0.6129 1950 0.1602 0.3448 0.6129 1951 −0.1612 0.6394 0.6129 1952 0.0992 0.4072 0.6129 1953 0.2339 −0.3461 0.6129 1954 0.0367 0.4681 0.6129 1955 0.3046 −0.3973 0.6129 1956 0.3352 0.1502 0.6129 1957 −0.0530 −0.1474 0.6129 1958 0.7146 −0.7228 0.6129 1959 0.3747 −0.4492 0.6129 1960 0.5554 −0.1207 0.6129 1961 0.8201 −0.4675 0.6129 1962 0.7800 −0.7805 0.6129 1963 0.4442 −0.5020 0.6129 1964 0.7676 −0.3978 0.6129 1965 0.5013 −0.0522 0.6129 1966 0.8445 −0.8393 0.6129 1967 0.5130 −0.5557 0.6129 1968 0.4467 0.0159 0.6129 1969 0.7149 −0.3282 0.6129 1970 0.9776 −0.6767 0.6129 1971 0.9082 −0.8990 0.6129 1972 0.5810 −0.6104 0.6129 1973 0.3914 0.0834 0.6129 1974 0.6621 −0.2588 0.6129 1975 0.9250 −0.6070 0.6129 1976 0.9710 −0.9596 0.6129 1977 0.6482 −0.6661 0.6129 1978 0.6089 −0.1896 0.6129 1979 0.8726 −0.5373 0.6129 1980 1.0331 −1.0209 0.6129 1981 1.0828 −0.8159 0.6129 1982 1.3485 −1.1620 0.6129 1983 1.5900 −1.5147 0.6129 1984 1.3977 −1.3967 0.6129 1985 1.0946 −1.0828 0.6129 1986 1.0301 −0.7463 0.6129 1987 1.2951 −1.0931 0.6129 1988 1.5626 −1.4377 0.6129 1989 1.4572 −1.4605 0.6129 1990 1.1557 −1.1451 0.6129 1991 1.2418 −1.0240 0.6129 1992 1.5095 −1.3685 0.6129 1993 1.5168 −1.5242 0.6129 1994 1.2166 −1.2075 0.6129 1995 1.1886 −0.9547 0.6129 1996 1.4559 −1.2996 0.6129 1997 1.2773 −1.2703 0.6129 1998 1.1356 −0.8854 0.6129 1999 1.4021 −1.2309 0.6129 2000 1.3377 −1.3333 0.6129 2001 −1.7281 0.7708 0.6452 2002 −1.7244 0.6891 0.6452 2003 −0.7671 0.3656 0.6452 2004 −1.1453 0.5709 0.6452 2005 −1.5683 0.6367 0.6452 2006 −1.5996 0.8834 0.6452 2007 −1.1921 1.0136 0.6452 2008 −0.7654 0.9740 0.6452 2009 −0.6953 0.3179 0.6452 2010 −1.0661 0.5370 0.6452 2011 −1.4821 0.6358 0.6452 2012 −1.6700 0.8338 0.6452 2013 −1.2774 1.0014 0.6452 2014 −0.8491 0.9949 0.6452 2015 −0.9889 0.4985 0.6452 2016 −1.3960 0.6312 0.6452 2017 −1.5234 0.9238 0.6452 2018 −1.3615 0.9825 0.6452 2019 −0.9340 1.0096 0.6452 2020 −0.9136 0.4565 0.6452 2021 −1.3107 0.6191 0.6452 2022 −1.4437 0.9567 0.6452 2023 −1.0199 1.0177 0.6452 2024 −0.8398 0.4119 0.6452 2025 −1.2269 0.5988 0.6452 2026 −1.6541 0.6440 0.6452 2027 −1.1060 1.0190 0.6452 2028 −0.6835 0.9473 0.6452 2029 −0.4129 0.1199 0.6452 2030 −0.3768 0.7911 0.6452 2031 −0.3429 0.0695 0.6452 2032 −0.4501 0.8365 0.6452 2033 −0.2732 0.0188 0.6452 2034 −0.6241 0.2693 0.6452 2035 −0.5257 0.8780 0.6452 2036 −0.2035 −0.0320 0.6452 2037 −0.5534 0.2199 0.6452 2038 −0.6035 0.9151 0.6452 2039 −0.2367 0.6906 0.6452 2040 −0.4830 0.1701 0.6452 2041 −0.3057 0.7423 0.6452 2042 0.0202 0.4608 0.6452 2043 0.3086 0.1406 0.6452 2044 0.2531 0.2066 0.6452 2045 −0.0415 0.5211 0.6452 2046 −0.1047 0.5797 0.6452 2047 0.1966 0.2717 0.6452 2048 −0.1698 0.6363 0.6452 2049 0.1391 0.3359 0.6452 2050 0.0803 0.3990 0.6452 2051 0.2781 −0.3958 0.6452 2052 −0.0648 −0.1344 0.6452 2053 0.3456 −0.4495 0.6452 2054 0.0043 −0.1860 0.6452 2055 0.0732 −0.2379 0.6452 2056 0.1418 −0.2901 0.6452 2057 0.2101 −0.3427 0.6452 2058 −0.1341 −0.0831 0.6452 2059 0.6103 −0.6705 0.6452 2060 0.5756 −0.1979 0.6452 2061 0.8344 −0.5427 0.6452 2062 0.6750 −0.7275 0.6452 2063 0.5232 −0.1294 0.6452 2064 0.7828 −0.4736 0.6452 2065 0.7390 −0.7853 0.6452 2066 0.4126 −0.5037 0.6452 2067 0.4704 −0.0613 0.6452 2068 0.7312 −0.4045 0.6452 2069 0.8023 −0.8439 0.6452 2070 0.4791 −0.5586 0.6452 2071 0.4171 0.0065 0.6452 2072 0.6795 −0.3355 0.6452 2073 0.9376 −0.6809 0.6452 2074 0.8649 −0.9031 0.6452 2075 0.5450 −0.6142 0.6452 2076 0.3632 0.0738 0.6452 2077 0.6277 −0.2666 0.6452 2078 0.8859 −0.6118 0.6452 2079 0.9269 −0.9630 0.6452 2080 1.0931 −0.8876 0.6452 2081 1.3559 −1.2294 0.6452 2082 1.4689 −1.5184 0.6452 2083 1.2910 −1.3306 0.6452 2084 0.9884 −1.0235 0.6452 2085 1.2311 −1.2685 0.6452 2086 1.0411 −0.8188 0.6452 2087 1.3029 −1.1614 0.6452 2088 1.5414 −1.5095 0.6452 2089 1.3504 −1.3931 0.6452 2090 1.0494 −1.0844 0.6452 2091 0.9893 −0.7499 0.6452 2092 1.2501 −1.0932 0.6452 2093 1.4095 −1.4558 0.6452 2094 1.1102 −1.1456 0.6452 2095 1.1975 −1.0248 0.6452 2096 1.4622 −1.3651 0.6452 2097 1.5149 −1.4334 0.6452 2098 1.1708 −1.2069 0.6452 2099 1.1452 −0.9563 0.6452 2100 1.4091 −1.2972 0.6452 2101 −0.8175 0.4524 0.6774 2102 −1.1952 0.6465 0.6774 2103 −1.6165 0.6979 0.6774 2104 −1.5036 0.9648 0.6774 2105 −1.0894 1.0493 0.6774 2106 −0.7472 0.4043 0.6774 2107 −1.5315 0.6924 0.6774 2108 −1.5792 0.9256 0.6774 2109 −1.0377 0.5820 0.6774 2110 −1.1745 1.0466 0.6774 2111 −0.7548 0.9921 0.6774 2112 −0.6780 0.3546 0.6774 2113 −1.4464 0.6898 0.6774 2114 −1.6487 0.8765 0.6774 2115 −1.2591 1.0368 0.6774 2116 −0.8365 1.0161 0.6774 2117 −0.9624 0.5421 0.6774 2118 −0.8891 0.4986 0.6774 2119 −1.3615 0.6829 0.6774 2120 −1.7041 0.8127 0.6774 2121 −1.3427 1.0201 0.6774 2122 −0.9198 1.0339 0.6774 2123 −1.1153 0.6172 0.6774 2124 −1.2775 0.6686 0.6774 2125 −1.6922 0.7329 0.6774 2126 −1.4244 0.9962 0.6774 2127 −1.0043 1.0451 0.6774 2128 −0.4744 0.2000 0.6774 2129 −0.6750 0.9622 0.6774 2130 −0.3109 0.7435 0.6774 2131 −0.4074 0.1474 0.6774 2132 −0.3791 0.7946 0.6774 2133 −0.3407 0.0944 0.6774 2134 −0.4495 0.8425 0.6774 2135 −0.2741 0.0412 0.6774 2136 −0.6096 0.3038 0.6774 2137 −0.5223 0.8868 0.6774 2138 −0.2077 −0.0122 0.6774 2139 −0.5418 0.2522 0.6774 2140 −0.5975 0.9269 0.6774 2141 −0.2449 0.6896 0.6774 2142 −0.1415 −0.0659 0.6774 2143 0.0014 0.4542 0.6774 2144 0.2524 −0.3918 0.6774 2145 0.2803 0.1323 0.6774 2146 −0.0754 −0.1197 0.6774 2147 0.1219 −0.2822 0.6774 2148 −0.0578 0.5155 0.6774 2149 0.3172 −0.4471 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0.9677 3038 −0.0138 −0.1037 0.9677 3039 −0.2508 0.2149 0.9677 3040 −0.2858 0.6334 0.9677 3041 −0.0525 0.3121 0.9677 3042 −0.2033 0.1512 0.9677 3043 −0.3346 0.6960 0.9677 3044 −0.0981 0.3771 0.9677 3045 0.1279 0.0507 0.9677 3046 0.0815 −0.2308 0.9677 3047 −0.1560 0.0874 0.9677 3048 0.0338 −0.1673 0.9677 3049 −0.3843 0.7579 0.9677 3050 −0.1442 0.4418 0.9677 3051 0.1293 −0.2942 0.9677 3052 0.0830 0.1162 0.9677 3053 −0.1086 0.0237 0.9677 3054 −0.3464 0.3416 0.9677 3055 −0.1907 0.5061 0.9677 3056 0.0380 0.1816 0.9677 3057 −0.0612 −0.0400 0.9677 3058 −0.2984 0.2784 0.9677 3059 0.7250 −1.0377 0.9677 3060 0.4709 −0.7327 0.9677 3061 0.3985 −0.3415 0.9677 3062 0.2255 −0.4205 0.9677 3063 0.2178 −0.0803 0.9677 3064 0.4440 −0.4066 0.9677 3065 0.6737 −0.7304 0.9677 3066 0.7771 −1.0977 0.9677 3067 0.4897 −0.4715 0.9677 3068 0.6222 −0.9167 0.9677 3069 0.5209 −0.7943 0.9677 3070 0.2740 −0.4834 0.9677 3071 0.1728 −0.0148 0.9677 3072 0.6275 −0.6658 0.9677 3073 0.5714 −0.8557 0.9677 3074 0.3227 −0.5461 0.9677 3075 0.3531 −0.2763 0.9677 3076 0.4212 −0.6708 0.9677 3077 0.3079 −0.2111 0.9677 3078 0.5355 −0.5364 0.9677 3079 0.7664 −0.8594 0.9677 3080 0.5814 −0.6012 0.9677 3081 0.6734 −0.9773 0.9677 3082 0.1773 −0.3574 0.9677 3083 0.2628 −0.1457 0.9677 3084 0.7200 −0.7949 0.9677 3085 0.3718 −0.6086 0.9677 3086 0.9354 −1.2757 0.9677 3087 0.9062 −1.0523 0.9677 3088 1.1429 −1.3710 0.9677 3089 0.8295 −1.1573 0.9677 3090 1.0428 −1.3927 0.9677 3091 0.8594 −0.9881 0.9677 3092 1.0974 −1.4503 0.9677 3093 0.8823 −1.2166 0.9677 3094 0.8128 −0.9238 0.9677 3095 1.0480 −1.2437 0.9677 3096 0.9531 −1.1163 0.9677 3097 1.0957 −1.3072 0.9677 3098 1.0003 −1.1802 0.9677 3099 1.1647 −1.4418 0.9677 3100 0.9889 −1.3344 0.9677 3101 −1.1205 1.1166 1.0000 3102 −1.4535 1.2961 1.0000 3103 −1.1047 1.3545 1.0000 3104 −1.0507 1.0794 1.0000 3105 −1.4137 1.2343 1.0000 3106 −1.1812 1.3743 1.0000 3107 −0.9835 1.0378 1.0000 3108 −1.3410 1.2033 1.0000 3109 −1.2596 1.3842 1.0000 3110 −0.9190 0.9921 1.0000 3111 −1.2663 1.1775 1.0000 3112 −1.3385 1.3814 1.0000 3113 −0.9599 1.2915 1.0000 3114 −1.1925 1.1492 1.0000 3115 −1.4140 1.3595 1.0000 3116 −1.0309 1.3264 1.0000 3117 −0.5296 0.6007 1.0000 3118 −0.4878 0.8758 1.0000 3119 −0.4799 0.5392 1.0000 3120 −0.8273 1.2058 1.0000 3121 −0.5398 0.9354 1.0000 3122 −0.6856 0.7792 1.0000 3123 −0.8921 1.2510 1.0000 3124 −0.5933 0.9936 1.0000 3125 −0.6322 0.7209 1.0000 3126 −0.7979 0.8906 1.0000 3127 −0.7408 0.8359 1.0000 3128 −0.6485 1.0502 1.0000 3129 −0.5803 0.6613 1.0000 3130 −0.7652 1.1568 1.0000 3131 −0.8572 0.9428 1.0000 3132 −0.7057 1.1047 1.0000 3133 −0.4372 0.8151 1.0000 3134 −0.4310 0.4771 1.0000 3135 −0.0548 −0.0313 1.0000 3136 −0.2877 0.2881 1.0000 3137 −0.2447 0.5643 1.0000 3138 −0.0178 0.2406 1.0000 3139 −0.0083 −0.0953 1.0000 3140 −0.2408 0.2244 1.0000 3141 −0.2916 0.6279 1.0000 3142 −0.0625 0.3058 1.0000 3143 −0.3350 0.3515 1.0000 3144 0.0382 −0.1592 1.0000 3145 −0.1942 0.1606 1.0000 3146 −0.1075 0.3708 1.0000 3147 0.0267 0.1752 1.0000 3148 −0.3827 0.4145 1.0000 3149 −0.3392 0.6910 1.0000 3150 −0.3877 0.7535 1.0000 3151 −0.1527 0.4356 1.0000 3152 0.1315 −0.2869 1.0000 3153 −0.1012 0.0327 1.0000 3154 −0.1477 0.0967 1.0000 3155 0.0848 −0.2231 1.0000 3156 0.0711 0.1098 1.0000 3157 −0.1984 0.5001 1.0000 3158 0.1783 −0.3506 1.0000 3159 0.2490 −0.1516 1.0000 3160 0.6112 −0.6701 1.0000 3161 0.4742 −0.4765 1.0000 3162 0.7032 −0.7987 1.0000 3163 0.7117 −1.0372 1.0000 3164 0.2253 −0.4141 1.0000 3165 0.2044 −0.0863 1.0000 3166 0.6571 −0.7344 1.0000 3167 0.7625 −1.0978 1.0000 3168 0.5130 −0.7913 1.0000 3169 0.2726 −0.4775 1.0000 3170 0.1599 −0.0210 1.0000 3171 0.5621 −0.8533 1.0000 3172 0.3201 −0.5407 1.0000 3173 0.4642 −0.7290 1.0000 3174 0.1155 0.0444 1.0000 3175 0.3386 −0.2819 1.0000 3176 0.3836 −0.3469 1.0000 3177 0.5654 −0.6057 1.0000 3178 0.6115 −0.9149 1.0000 3179 0.3678 −0.6037 1.0000 3180 0.4288 −0.4118 1.0000 3181 0.2937 −0.2168 1.0000 3182 0.5197 −0.5412 1.0000 3183 0.7493 −0.8629 1.0000 3184 0.6614 −0.9763 1.0000 3185 0.4159 −0.6665 1.0000 3186 1.0284 −1.2465 1.0000 3187 0.9346 −1.1192 1.0000 3188 1.1433 −1.4447 1.0000 3189 0.8881 −1.0553 1.0000 3190 1.1219 −1.3740 1.0000 3191 0.8417 −0.9912 1.0000 3192 1.0228 −1.3953 1.0000 3193 1.0754 −1.3101 1.0000 3194 1.0765 −1.4533 1.0000 3195 0.8138 −1.1580 1.0000 3196 0.7955 −0.9271 1.0000 3197 0.9175 −1.2774 1.0000 3198 0.8654 −1.2179 1.0000 3199 0.9699 −1.3366 1.0000 3200 0.9813 −1.1830 1.0000

It will also be appreciated that the airfoil disclosed in the above Table I may be scaled up or down geometrically for use in other similar turbine designs. Consequently, the coordinate values set forth in Table I may be scaled upwardly or downwardly such that the airfoil profile shape remains unchanged. A scaled version of the coordinates in Table I would be represented by X, Y and Z′ coordinate values of Table I, with X and Y and the non-dimensional Z′ coordinate value converted to inches, multiplied or divided by a constant number.

An important term in this disclosure is profile. The profile is the range of the variation between measured points on an airfoil surface and the ideal position listed in Table I. The actual profile on a manufactured blade will be different then those in Table I and the design is robust to this variation meaning that mechanical and aerodynamic function are not impaired. As noted above, a + or −0.06 inch profile tolerance is used herein.

The disclosed airfoil shape optimizes and is specific to the machine conditions and specifications. It provides a unique profile to achieve 1) interaction between other stages in the high pressure turbine; 2) aerodynamic efficiency; and 3) normalized aerodynamic and mechanical blade loadings. The disclosed loci of points allow the 7FB IGCC gas turbine to run in an efficient, safe and smooth manner. As also noted, any scale of the disclosed airfoil may be adopted as long as 1) interaction between other stages in the high pressure turbine; 2) aerodynamic efficiency; and 3) normalized aerodynamic and mechanical blade loadings are maintained in the scaled turbine.

While the invention has been described in connection with what is presently considered to be the most practical and preferred embodiment, it is to be understood that the invention is not to be limited to the disclosed embodiment, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims. 

1. A turbine bucket including a bucket airfoil having an airfoil shape, said airfoil having a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z′ set forth in Table I wherein the Z′ values are non-dimensional values from 0 to 1 convertible to Z distances in inches by multiplying the Z′ values by a height of the airfoil in inches and adding the radius of the airfoil base, and wherein X and Y are distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z, the profile sections at the Z distances being joined smoothly with one another to form a complete airfoil shape.
 2. A turbine bucket according to claim 1, forming part of a third stage of a turbine.
 3. A turbine bucket according to claim 1, wherein said airfoil shape lies in an envelope within +/−0.060 inches in a direction normal to any airfoil surface location.
 4. A turbine bucket according to claim 1, wherein the height of the turbine bucket from root to tip is 17.6136 inches.
 5. A turbine bucket including a bucket airfoil having an uncoated nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y and Z′ set forth in Table I wherein the Z′ values are non-dimensional values from 0 to 1 convertible to Z distances in inches by multiplying the Z′ values by a height of the airfoil in inches and adding the radius of the airfoil base, and wherein X and Y are distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each Z distance, the profile sections at the Z distances being joined smoothly with one another to form a complete airfoil shape, the X, Y and Z distances being scalable as a function of the same constant or number to provide a scaled-up or scaled-down airfoil.
 6. A turbine bucket according to claim 5, forming part of a third stage of a turbine.
 7. A turbine bucket according to claim 5, wherein said airfoil shape lies in an envelope within +/−0.060 inches in a direction normal to any airfoil surface location.
 8. A turbine bucket according to claim 5, wherein the height of the turbine bucket from root to tip is 17.6136 inches.
 9. A turbine comprising a turbine wheel having a plurality of buckets, each of said buckets including an airfoil having an airfoil shape, said airfoil having a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z′ set forth in Table I wherein the Z′ values are non-dimensional values from 0 to 1 convertible to Z distances in inches by multiplying the Z′ values by a height of the airfoil in inches and adding the radius of the airfoil base, and wherein X and Y are distances in inches which, when connected by smooth continuing arcs, define the airfoil profile sections at each distance Z, the profile sections at the Z distances being joined smoothly with one another to form a complete airfoil shape.
 10. A turbine according to claim 9, wherein the turbine wheel comprises a third stage of the turbine.
 11. A turbine according to claim 9, wherein X represents a distance parallel to the turbine axis of rotation.
 12. A turbine according to claim 9, wherein the height of the turbine bucket from root to tip is 17.6136 inches.
 13. A turbine according to claim 9, wherein the Z height between an axial centerline of said turbine wheel and a base of the airfoil as defined in Table 1 is 37.3182 inches and which corresponds to the non-dimensionalized Z (Z′) at 0.000.
 14. A turbine according to claim 13, wherein the height of the turbine bucket from root to tip is 17.6136 inches.
 15. A turbine according to claim 9, wherein the X, Y and Z distances are scalable as a function of the same constant or number to provide a scaled-up or scaled-down bucket airfoil.
 16. A turbine according to claim 15, wherein the turbine wheel comprises a third stage of the turbine.
 17. A turbine according to claim 15, wherein X represents a distance parallel to the turbine axis of rotation.
 18. A turbine according to claim 15, wherein the height of the turbine bucket from root to tip is 17.6136 inches.
 19. A turbine according to claim 15, wherein the Z height between an axial centerline of said turbine wheel and a base of the airfoil as defined in Table 1 is 37.3182 inches and which corresponds to the non-dimensionalized Z (Z′) at 0.000.
 20. A turbine according to claim 15, said airfoil shape lying in an envelope within +/−0.060 inches in a direction normal to any airfoil surface location. 